An important question raised when filamentary structure was first
observed in radio galaxies was whether the volume filling factor for
radio emitting fluid in the lobes could be very low.
Perley et al. (1984)
estimate that the volume filling for the lobes of Cygnus A could
be between 0.03 and 0.3. On the other hand, detailed analysis of
surface brightness profiles of the lobes shows that there is a
space filling diffuse component
(Carilli 1989,
Leahy 1991).
Although
noticeable to the eye, the surface brightness contrast between the
filaments and the background is typically
20% at 4.5 GHz, with
a few filaments contrasting by up to 50%. If the filaments are
rope-like (one dimensional) their minimum pressures are typically about
a factor four larger than their environments, while if they are
sheet-like (two dimensional) they are only over-pressured by 30% or so.

Many explanations have been considered for filaments in radio sources,
including cooling instabilities
(Eilek 1989),
regions of anomalous resistive reconnection
(Eilek 1989,
Hines et al. 1990,
Christiansen 1989),
turbulent vortices in back-flow in the radio lobe
(Norman et al. 1982),
and weak shocks, or non-linear (Mach 1) acoustic waves driven by
the pressure difference between the hotspots and lobes
(Carilli 1989).

The most recent and convincing explanation of filamentary structure in
radio galaxies is that coming from the 3D simulations of
Clarke (1992)
which include passive magnetic fields. He finds the natural development
of rope-like filaments in radio lobes corresponding to regions of
enhanced, or `bundled' magnetic field. Importantly, he notes no
evidence for enhanced thermal densities or pressures in these regions.
The intermittent bundles of enhanced field occur in regions of large
velocity shear implying a simple kinematic dynamo process as the origin
for the enhanced (although still dynamically weak)
field regions. The polarization characteristics of these
filaments are consistent with that observed for Cygnus A (high fractional
polarization with longitudinal fields).

A possible physical diagnostic for filamentary structure in radio lobes
is the power spectrum.
Carilli (1989)
measured a power-law power
spectrum of the form: P(k)
k-2.6, on spatial
scales (= 1/k) between 0.7" and 8".
Eilek (1989)
shows that an observed
power-spectrum of index -3
might result from isotropic, weak-field Kolmogorov turbulence.

DeGraff (1992)
has performed a fractal analysis of the filaments in
Cygnus A. He obtains a fractal dimension between 0.4 and 1.2,
consistent with the elongated appearance of the structures.
DeGraff and
Christiansen (1996)
show that the fractal spectra of the filamentary
structure in the lobes of Cygnus A are best reproduced with turbulent
models involving spatial variations in both the fields and the
relativistic particles.